Simple Interest
MCQs Math


Question:     William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.


Correct Answer  8

Solution And Explanation

Solution

Given,

Principal (P) = $5000

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $8600

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $8600 – $5000 = $3600

Thus, Simple Interest = $3600

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = 100 × Simple Interest/Principal × Rate of Interest

⇒ T = 100 × SI/P × R

Thus, Time (T) = 100 × 3600/5000 × 9

= 360000/45000

= 8 years (using formula)

Thus, Time (T) = 8 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $5000

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $3600 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 9% of Principal

= 9% of $5000

= 9/100 × 5000

= 9 × 5000/100

= 45000/100 = 450

Thus, simple Interest for 1 year = $450

Now,

∵ If the simple Interest is $450, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/450 years

∴ If the simple Interest is $3600, then the time = 1/450 × 3600 years

= 1 × 3600/450 years

= 3600/450 = 8 years

Thus, time (T) = 8 years Answer


Similar Questions

(1) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 2% simple interest?

(2) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 5% simple interest?

(3) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?

(4) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 3 years.

(5) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 9% simple interest?

(6) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5960 to clear the loan, then find the time period of the loan.

(7) How much loan did Mary borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6060 to clear it?

(8) How much loan did Linda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6420 to clear it?

(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 8 years.

(10) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.


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